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5x(2+x)=45+5x
We move all terms to the left:
5x(2+x)-(45+5x)=0
We add all the numbers together, and all the variables
5x(x+2)-(5x+45)=0
We multiply parentheses
5x^2+10x-(5x+45)=0
We get rid of parentheses
5x^2+10x-5x-45=0
We add all the numbers together, and all the variables
5x^2+5x-45=0
a = 5; b = 5; c = -45;
Δ = b2-4ac
Δ = 52-4·5·(-45)
Δ = 925
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{925}=\sqrt{25*37}=\sqrt{25}*\sqrt{37}=5\sqrt{37}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{37}}{2*5}=\frac{-5-5\sqrt{37}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{37}}{2*5}=\frac{-5+5\sqrt{37}}{10} $
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